Compute the curl:
Compute the divergence:
A conservative vector field has zero curl, which is not the case here, so is not conservative.
We can also employ the same method as I showed in an earlier question of yours [28193504]. We want to find a scalar function whose gradient is , so
However, there is no function that depends only on and that satisfies this partial differential equation; to wit, we cannot eliminate . So no such exists.